If an equation of a line in slope-intercept form (y=mx+b) has no x variable, this means that the slope is 0. Any number being multiplied by 0 equals 0. When m=0, this means that the "mx" portion of the line's equation is 0. The result is that y=b. Remember that a line with a slope of 0 is a horizontal line.
When I’m asked to find the slope of the equation of a line, I’m a happy camper if the line is in y equals mx plus b form because in y equals mx plus b form, the slope number is just the coefficient in front of x.
This equation is kind of in y equals mx plus b form. The trick is that there is no x. If you can’t tell what the slope is right away, what if I give you this hint. I’m just going to rewrite the same equation only I stack in zero Xs right? There’s no Xs in that problem, now can you see what the slope is?
There it is the slope of this equation is just zero and the way I know this if I didn’t go through and put in the y equals mx plus b form, is because the line y equals 4 is a horizontal line that passes through 4 like that, and there’s no vertical change. That means that slope value is zero.
So when you see an equation like this where there is only one letter, and you’re asked to find the slope of it, you have a couple of options. One option is to try to write it in y equals mx plus b form and look for the coefficient of x. The other way is to try to graph it and see if that helps you, or if you’re a good memorizer sometimes people just memorize, if it’s y equals mh, like well some constant, that means you’re slope is always going to be zero and it’s always going to be a horizontal line.
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